Graphs Breadth First Search
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1 Grp Brdt Frt Sr SFO ORD LAX DFW - 1 -
2 Outo Ø By undrtndn t tur, you oud to: q L rp ordn to t ordr n w vrt r dovrd n rdt-rt r. q Idnty t urrnt tt o rdt-rt r n tr o vrt tt r prvouy dovrd, ut dovrd or undovrd. q Idnty t ontnt o t rdt-rt r quu t ny tt o t r. q Ipnt rdt-rt r q Dontrt p ppton o rdt-rt r - 2 -
3 Outn Ø BFS Aort Ø BFS Appton: Sortt Pt on n unwtd rp - 3 -
4 Outn Ø BFS Aort Ø BFS Appton: Sortt Pt on n unwtd rp - 4 -
5 Brdt-Frt Sr Ø Brdt-rt r (BFS) nr tnqu or trvrn rp Ø A BFS trvr o rp G q Vt t vrt nd d o G q Dtrn wtr G onntd q Coput t onntd oponnt o G q Coput pnnn ort o G Ø BFS on rp wt V vrt nd E d t O( V + E ) t Ø BFS n urtr xtndd to ov otr rp pro q Cy dtton q Fnd nd rport pt wt t nu nur o d twn two vn vrt - 5 -
6 BFS Aort Pttrn BFS(G,) Prondton: G rp, vrtx n G Potondton: vrt n G r ro v n vtd or vrtx u V[G] oor[u] BLACK //ntz vrtx oour[] RED Q.nquu() w Q u Q.dquu() or v Ad[u] //xpor d (u,v) oor[v] = BLACK oour[v] RED Q.nquu(v) oour[u] GRAY - 6 -
7 BFS Lv-Ordr Trvr Ø Not tt n BFS xporton t p on wvront ontn o nod tt r t dtn ro t our. Ø W n t uv wvront y tr dtn: L 0, L 1, - 7 -
8 BFS Exp A A undovrd dovrd (on Quu) A A nd unxpord d L 1 B C D dovry d ro d E F L 0 A L 0 A L 1 B C D L 1 B C D E F E F - 8 -
9 BFS Exp (ont.) L 0 A L 0 A L 1 B C D L 1 B C D E F L 2 E F L 0 A L 0 A L 1 B C D L 1 B C D L 2 E F L 2 E F - 9 -
10 BFS Exp (ont.) L 0 A L 0 A L 1 B C D L 1 B C D L 2 E F L 2 E F L 0 A L 1 B C D L 2 E F
11 Proprt Notton G : onntd oponnt o Proprty 1 BFS(G, ) vt t vrt nd d o G Proprty 2 T dovry d d y BFS(G, ) or pnnn tr T o G Proprty 3 For vrtx v n L q T pt o T ro to v d q Evry pt ro to v n G t t d L 1 B L 0 B L 2 A E A E C C F F D D
12 Any Ø Sttn/ttn vrtx/d t O(1) t Ø E vrtx d tr t q on BLACK (undovrd) q on RED (dovrd, on quu) q on GRAY (nd) Ø E d ondrd tw (or n undrtd rp) Ø E vrtx pd on t quu on Ø Tu BFS run n O( V + E ) t provdd t rp rprntd y n dny t trutur
13 Appton Ø BFS trvr n pzd to ov t oown pro n O( V + E ) t: q Coput t onntd oponnt o G q Coput pnnn ort o G q Fnd p y n G, or rport tt G ort q Gvn two vrt o G, nd pt n G twn t wt t nu nur o d, or rport tt no u pt xt
14 Outn Ø BFS Aort Ø BFS Appton: Sortt Pt on n unwtd rp
15 Appton: Sortt Pt on n Unwtd Grp Ø Go: To rovr t ortt pt ro our nod to otr r nod v n rp. q T nt o pt nd t pt tv r rturnd. Ø Not: q Tr r n xponnt nur o po pt q Anoou to v ordr trvr or tr q T pro rdr or nr rp tn tr u o y!?
16 Brdt-Frt Sr Input: Grp G = ( V, E) (drtd or undrtd) nd our vrtx Î V. Output: dv [ ] = ortt pt dtn d ( v, ) ro to v, " vî V. p [ v] = u u tt ( u, v) t d on ortt pt ro to v. Ø Id: nd out r wv ro. Ø Kp tr o pror y oourn vrt: q Undovrd vrt r oourd q Jut dovrd vrt (on t wvront) r oourd rd. q Prvouy dovrd vrt (nd wvront) r oourd ry
17 BFS Aort wt Dtn nd Prdor BFS(G,) Prondton: G rp, vrtx n G Potondton: d[u] = ortt dtn δ [u] nd π[u] = prdor o u on ortt pt ro to vrtx u n G or vrtx u V[G] d[u] π[u] nu oor[u] = BLACK //ntz vrtx oour[] RED d[] 0 Q.nquu() w Q u Q.dquu() or v Ad[u] //xpor d (u,v) oor[v] = BLACK oour[v] RED d[v] d[u] + 1 π[v] u oour[u] GRAY Q.nquu(v)
18 BFS Frt-In Frt-Out (FIFO) quu tor ut dovrd vrt Found Not Hndd Quu d
19 d BFS Found Not Hndd Quu
20 d BFS Found Not Hndd Quu d
21 d BFS Found Not Hndd Quu d
22 d BFS Found Not Hndd Quu d
23 d BFS Found Not Hndd Quu
24 d BFS Found Not Hndd Quu
25 d BFS Found Not Hndd Quu
26 d BFS Found Not Hndd Quu
27 d BFS d=3 Found Not Hndd Quu d=3
28 d BFS d=3 Found Not Hndd Quu d=3
29 d BFS d=3 Found Not Hndd Quu d=3
30 d BFS d=3 Found Not Hndd Quu d=3
31 d BFS d=3 Found Not Hndd Quu d=3
32 d BFS d=3 Found Not Hndd Quu d=3
33 d d=4 BFS d=3 Found Not Hndd Quu d=3 d=4
34 d d=4 BFS d=3 Found Not Hndd Quu d=3 d=4
35 d d=4 BFS d=3 Found Not Hndd Quu d=3 d=4
36 d d=4 BFS d=3 Found Not Hndd Quu d=4
37 d d=4 BFS d=3 Found Not Hndd Quu d=4 d=5
38 BFS(G,) Brdt-Frt Sr Aort: Proprt Prondton: G rp, vrtx n G Potondton: d[u] = ortt dtn δ[u] nd π[u] = prdor o u on ortt pt ro to vrtx u n G or vrtx u V[G] d[u] π[u] nu oor[u] = BLACK //ntz vrtx oour[] RED d[] 0 Q.nquu() w Q u Q.dquu() or v Ad[u] //xpor d (u,v) oor[v] = BLACK oour[v] RED d[v] d[u] + 1 π[v] u oour[u] GRAY Q.nquu(v) Ø Q FIFO quu. Ø E vrtx nd nt d vu t ot on. Ø Q ontn vrt wt d vu {,,, +1,, +1} Ø d vu nd r onotony nrn ovr t.
39 Brdt-Frt-Sr Grdy Ø Vrt r ndd (nd nd): q n ordr o tr dovry (FIFO quu) q St d vu rt
40 Outn Ø BFS Aort Ø BFS Appton: Sortt Pt on n unwtd rp
41 Outo Ø By undrtndn t tur, you oud to: q L rp ordn to t ordr n w vrt r dovrd n rdt-rt r. q Idnty t urrnt tt o rdt-rt r n tr o vrt tt r prvouy dovrd, ut dovrd or undovrd. q Idnty t ontnt o t rdt-rt r quu t ny tt o t r. q Ipnt rdt-rt r q Dontrt p ppton o rdt-rt r
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Grp Dpt Frt Sr SFO 337 LAX 1843 1743 1233 802 DFW ORD - 1 - Grp Sr Aort - 2 - Outo Ø By unrtnn t tur, you ou to: q L rp orn to t orr n w vrt r ovr, xpor ro n n n pt-rt r. q Cy o t pt-rt r tr,, orwr n ro
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